Zobrazeno 1 - 10
of 24
pro vyhledávání: '"P. V. Nevskii"'
Autor:
Mikhail V. Nevskii
Publikováno v:
Моделирование и анализ информационных систем, Vol 31, Iss 3, Pp 316-337 (2024)
We give some estimates for the minimum projector norm under linear interpolation on a compact set in ${\mathbb R}^n$. Let $\Pi_1({\mathbb R}^n)$ be the space of polynomials in $n$ variables of degree at most $1$, $\Omega$ is a compactum in ${\mathbb
Externí odkaz:
https://doaj.org/article/23712bcfb72841ffad5c838c5183e8e7
Autor:
Mikhail V. Nevskii, Alexey Y. Ukhalov
Publikováno v:
Моделирование и анализ информационных систем, Vol 30, Iss 3, Pp 246-257 (2023)
Suppose $\Omega$ is a closed bounded subset of ${\mathbb R}^n,$ $S$ is an $n$-dimensional non-degenerate simplex, $\xi(\Omega;S):=$ min {$\sigma\geqslant 1: \Omega\subset \sigma S$}. Here $\sigma S$ is the result of homothety of $S$ with respect to t
Externí odkaz:
https://doaj.org/article/0d537678edb743b4b9e950b479eab281
Autor:
Mikhail V. Nevskii
Publikováno v:
Моделирование и анализ информационных систем, Vol 29, Iss 2, Pp 92-103 (2022)
Let $Q_n=[0,1]^n$ be the unit cube in ${\mathbb R}^n$ and let $C(Q_n)$ be a space of continuous functions $f:Q_n\to{\mathbb R}$ with the norm $\|f\|_{C(Q_n)}:=\max_{x\in Q_n}|f(x)|.$ By $\Pi_1\left({\mathbb R}^n\right)$ denote a set of polynomials in
Externí odkaz:
https://doaj.org/article/b1adcd9e5a4a433090cdc3155d5e768a
Autor:
Mikhail V. Nevskii
Publikováno v:
Моделирование и анализ информационных систем, Vol 26, Iss 3, Pp 441-449 (2019)
Suppose \(n\in {\mathbb N}\). Let \(B_n\) be a Euclidean unit ball in \({\mathbb R}^n\) given by the inequality \(\|x\|\leq 1\), \(\|x\|:=\left(\sum\limits_{i=1}^n x_i^2\right)^{\frac{1}{2}}\). By \(C(B_n)\) we mean a set of continuous functions \(f:
Externí odkaz:
https://doaj.org/article/d4128880738446af92b91ccc167e65ee
Autor:
Mikhail V. Nevskii, Alexey Yu. Ukhalov
Publikováno v:
Моделирование и анализ информационных систем, Vol 26, Iss 2, Pp 279-296 (2019)
For \(x^{(0)}\in{\mathbb R}^n, R>0\), by \(B=B(x^{(0)};R)\) we denote a Euclidean ball in \({\mathbb R}^n\) given by the inequality \(\|x-x^{(0)}\|\leq R\), \(\|x\|:=\left(\sum_{i=1}^n x_i^2\right)^{1/2}\). Put \(B_n:=B(0,1)\). We mean by \(C(B)\) th
Externí odkaz:
https://doaj.org/article/3aba62dec1484c89836cde58bfd4ca77
Autor:
Mikhail V. Nevskii
Publikováno v:
Моделирование и анализ информационных систем, Vol 25, Iss 6, Pp 680-691 (2018)
Let \(C\) be a convex body and let \(S\) be a nondegenerate simplex in \({\mathbb R}^n\). Denote by \(\tau S\) the image of \(S\) under homothety with a center of homothety in the center of gravity of \(S\) and the ratio \(\tau\). We mean by \(\xi(C;
Externí odkaz:
https://doaj.org/article/59d7df89f7a64f3e8a9084448610ac87
Autor:
Mikhail V. Nevskii, Alexey Yu. Ukhalov
Publikováno v:
Моделирование и анализ информационных систем, Vol 25, Iss 3, Pp 291-311 (2018)
Let \(n\in{\mathbb N}\), and let \(Q_n\) be the unit cube \([0,1]^n\). By \(C(Q_n)\) we denote the space of continuous functions \(f:Q_n\to{\mathbb R}\) with the norm \(\|f\|_{C(Q_n)}:=\max\limits_{x\in Q_n}|f(x)|,\) by \(\Pi_1\left({\mathbb R}^n\rig
Externí odkaz:
https://doaj.org/article/69290d6f3b3b4df1a5278e17eed0927b
Autor:
Mikhail V. Nevskii, Alexey Y. Ukhalov
Publikováno v:
Моделирование и анализ информационных систем, Vol 25, Iss 1, Pp 140-150 (2018)
Let \(n\in{\mathbb N}\) and let \(Q_n\) be the unit cube \([0,1]^n\). For a nondegenerate simplex \(S\subset{\mathbb R}^n\), by \(\sigma S\) denote the homothetic copy of \(S\) with center of homothety in the center of gravity of \(S\) and ratio of h
Externí odkaz:
https://doaj.org/article/5588b755fc5a4abeb97175a1f5c21e8c
Autor:
Mikhail V. Nevskii, Alexey Y. Ukhalov
Publikováno v:
Моделирование и анализ информационных систем, Vol 24, Iss 5, Pp 578-595 (2017)
Let \(n\in{\mathbb N}\), \(Q_n=[0,1]^n.\) For a nondegenerate simplex \(S\subset {\mathbb R}^n\), by \(\sigma S\) we denote the homothetic image of \(S\) with the center of homothety in the center of gravity of \(S\) and ratio of homothety \(\sigma\)
Externí odkaz:
https://doaj.org/article/9293a5223c4142f39ee71a71f75883cf
Autor:
Mikhail V. Nevskii, Alexey Yu. Ukhalov
Publikováno v:
Моделирование и анализ информационных систем, Vol 24, Iss 1, Pp 94-110 (2017)
Let \(n\in {\mathbb N}\) and \(Q_n=[0,1]^n\). For a nondegenerate simplex \(S\subset {\mathbb R}^n\), by \(\sigma S\) we denote the homothetic copy of~\(S\) with center of homothety in the center of gravity of \(S\) and ratio of~homothety \(\sigma\).
Externí odkaz:
https://doaj.org/article/0fc3b7aed04f45daa956e02e97b7cf35